Try using this idea to find the sum of the first thirteen, fourteen, and fifteen
numbers.

Develop this idea with the class. Have groups work on reducing this to a formula.

Try not to reveal the formula: push the class towards higher numbers of sums. The
formula is: (the highest number)(the highest number plus one) then divide by two

n(n+1)/2 or nČ + n
2

This is called a quadratic equation or second degree equation. What is the greatest
common factor? Factor it out.

Produce a table of values of for y = (nČ + n)/2 from -5 to 5. Make a graph with n on
the x-axis and y on the y-axis. Note that graphing has NOT been specifically taught prior
to this point, unless the golf ball labs preceded this laboratory. This work proceeds with
the assumption that students have done math in the past. During such a class I circulate
and provide individual assistance as necessary.